LINEAR ALGEBRA
| Title | ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ / LINEAR ALGEBRA |
| Code | 131 |
| Faculty | Engineering |
| School | Mechanical Engineering |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Coordinator | Vasileios Rothos |
| Common | Yes |
| Status | Active |
| Course ID | 600014332 |
Programme of Study: UPS of School of Mechanical Engineering
Registered students: 308
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Compulsory Course | 1 | 1 | 4 |
| Academic Year | 2019 – 2020 |
| Class Period | Winter |
| Faculty Instructors |
|
| Instructors from Other Categories | |
| Weekly Hours | 3 |
| Class ID | 600149879
|
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600149879
- eLearning (Moodle):
Language of Instruction
- Greek (Instruction, Examination)
Learning Outcomes
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences, natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of the most widely taught subjects in college-level mathematics (and increasingly in high school).
After successfully completing the course, you will have a good understanding of the following topics and their applications:
Systems of linear equations
Row reduction and echelon forms
Matrix operations, including inverses
Block matrices
Linear dependence and independence
Subspaces and bases and dimensions
Orthogonal bases and orthogonal projections
Gram-Schmidt process
Linear models and least-squares problems
Determinants and their properties
Cramer's Rule
Eigenvalues and eigenvectors
Diagonalization of a matrix
Symmetric matrices
Positive definite matrices
Similar matrices
Linear transformations
Singular Value Decomposition
General Competences
- Apply knowledge in practice
- Work autonomously
- Work in teams
Course Content (Syllabus)
Cartesian products, mathematical induction. Matrices, linear transformations on real n-space,solving linear algebraic systems, linear independence and dimension, bases and coordinates, determinants, orthogonal projections, least squares, eigenvalues and eigenvectors and their applications to quadratic forms. Complex eigenvalues and eigenvectors are also covered in the 2 by 2 and 3 by 3 cases.
Keywords
matrices linear systems bases vector spaces eignevalues eigenvectors quadratic forms applications
Educational Material Types
- Notes
- Slide presentations
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
Description
projector PC
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 72 | 2.4 | |||
| Tutorial | 20 | 0.7 | |||
| Interactive Teaching in Information Center | 20 | 0.7 | |||
| Written assigments | 5 | 0.2 | |||
| Exams | 3 | 0.1 | |||
| Total | 120 | 4 |
Student Assessment
Description
Final exam 3hrs
Student Assessment methods
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Βιβλίο [2898]: ΕΙΣΑΓΩΓΗ ΣΤΗ ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ, GILBERT STRANG
Βιβλίο [204]: ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ ΚΑΙ ΕΦΑΡΜΟΓΕΣ, STRANG GILBERT
Βιβλίο [33314]: Εισαγωγή στη ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ, Θεδοδώρα Θεοχάρη-Αποστολίδη, Χαρά Χαραλάμπους, Χαρίλαος Βαβατσούλας
Βιβλίο [4649]: ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ ΚΑΙ ΑΝΑΛΥΤΙΚΗ ΓΕΩΜΕΤΡΙΑ, ΦΙΛΙΠΠΟΣ Ι. ΞΕΝΟΣ Λεπτομέρειες
Last Update
09-06-2020
